Finite Group Databasebeta

← Group #67465

Character table — Group #67465

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222222244444444444444888888888888121212121212121224242424
order12223444444666888812121212881212121224242424242424248888242424242424242416161616161616162244
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-111-1-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111-1-111-1-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111-1-111-1-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111-1-111-1-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ911-1-11i−i1-1i−i1-1-1ii−i−iii−i−i1-1i−i1-111-1-1ii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1i−i
χ1011-1-11i−i1-1i−i1-1-1ii−i−iii−i−i1-1i−i1-111-1-1ii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-11−ii
χ1111-1-11i−i1-1i−i1-1-1ii−i−iii−i−i1-1i−i1-111-1-1ii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-11−ii
χ1211-1-11i−i1-1i−i1-1-1ii−i−iii−i−i1-1i−i1-111-1-1ii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1i−i
χ1311-1-11−ii1-1−ii1-1-1−i−iii−i−iii1-1−ii1-111-1-1−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1−ii
χ1411-1-11−ii1-1−ii1-1-1−i−iii−i−iii1-1−ii1-111-1-1−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-11i−i
χ1511-1-11−ii1-1−ii1-1-1−i−iii−i−iii1-1−ii1-111-1-1−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-11i−i
χ1611-1-11−ii1-1−ii1-1-1−i−iii−i−iii1-1−ii1-111-1-1−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ii
χ1722222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222-2-2-2-22220000-2-2-2-20022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ192222222-2-2-2-22220000-2-2-2-20022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222-2-222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000
χ2122222-2-2-2-2222220000222200-2-2-2-2000000000000000000002−22−2−22−220000
χ2222222-2-2-2-2222220000222200-2-2-2-200000000000000000000−22−222−22−20000
χ232222-1222222-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ242222-1222222-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ252222-1222222-1-1-1-2-2-2-2-1-1-1-1-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ262222-1222222-1-1-1-2-2-2-2-1-1-1-1-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ272222-1-2-222-2-2-1-1-122221111-2-211-1-11111-1-1-1-100003−33−3−33−33000000000000
χ282222-1-2-222-2-2-1-1-122221111-2-211-1-11111-1-1-1-10000−33−333−33−3000000000000
χ292222-1-2-222-2-2-1-1-1-2-2-2-211112211-1-1-1-1-1-111112i2i−2i−2i−i−i−i−iiiii000000000000
χ302222-1-2-222-2-2-1-1-1-2-2-2-211112211-1-1-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i000000000000
χ3122-2-222i−2i2-22i−2i2-2-2−2i−2i2i2i2i2i−2i−2i-222i−2i2-2-2-222−2i−2i2i2i000000000000000000000000
χ3222-2-222i−2i-22−2i2i2-2-20000−2i−2i2i2i002i−2i-22000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ3322-2-222i−2i-22−2i2i2-2-20000−2i−2i2i2i002i−2i-2200000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ3422-2-22−2i2i2-2−2i2i2-2-22i2i−2i−2i−2i−2i2i2i-22−2i2i2-2-2-2222i2i−2i−2i000000000000000000000000
χ3522-2-22−2i2i-222i−2i2-2-200002i2i−2i−2i00−2i2i-22000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ3622-2-22−2i2i-222i−2i2-2-200002i2i−2i−2i00−2i2i-2200000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ3722-2-2-12i−2i2-22i−2i-1112i2i−2i−2i−i−iii2-2−ii-11-1-111−i−iii2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000
χ3822-2-2-12i−2i2-22i−2i-1112i2i−2i−2i−i−iii2-2−ii-11-1-111−i−iii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000
χ3922-2-2-12i−2i2-22i−2i-111−2i−2i2i2i−i−iii-22−ii-1111-1-1ii−i−i0000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000
χ4022-2-2-12i−2i2-22i−2i-111−2i−2i2i2i−i−iii-22−ii-1111-1-1ii−i−i0000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000
χ4122-2-2-1−2i2i2-2−2i2i-1112i2i−2i−2iii−i−i-22i−i-1111-1-1−i−iii0000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000
χ4222-2-2-1−2i2i2-2−2i2i-1112i2i−2i−2iii−i−i-22i−i-1111-1-1−i−iii0000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000
χ4322-2-2-1−2i2i2-2−2i2i-111−2i−2i2i2iii−i−i2-2i−i-11-1-111ii−i−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000
χ4422-2-2-1−2i2i2-2−2i2i-111−2i−2i2i2iii−i−i2-2i−i-11-1-111ii−i−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000
χ454444-244-4-4-4-4-2-2-20000222200-2-22200000000000000000000000000000000
χ464444-2-4-4-4-444-2-2-20000-2-2-2-200222200000000000000000000000000000000
χ4744-4-4-24i−4i-44−4i4i-22200002i2i−2i−2i00−2i2i2-200000000000000000000000000000000
χ4844-4-4-2−4i4i-444i−4i-2220000−2i−2i2i2i002i−2i2-200000000000000000000000000000000
χ494-44-44000000-44-4−2i22i2−2i22i200000000000000−2i22i2−2i22i2000000000000000000000000
χ504-44-44000000-44-42i2−2i22i2−2i2000000000000002i2−2i22i2−2i2000000000000000000000000
χ514-44-4-20000002-22−2i22i2−2i22i2−2i32i3−2i32i30000006−66−6i2−i2i2−i2000000000000000000000000
χ524-44-4-20000002-22−2i22i2−2i22i22i3−2i32i3−2i3000000−66−66i2−i2i2−i2000000000000000000000000
χ534-44-4-20000002-222i2−2i22i2−2i2−2i32i3−2i32i3000000−66−66−i2i2−i2i2000000000000000000000000
χ544-44-4-20000002-222i2−2i22i2−2i22i3−2i32i3−2i30000006−66−6−i2i2−i2i2000000000000000000000000
χ554-4-444000000-4-4422−22−22220000000000000022−22−2222000000000000000000000000
χ564-4-444000000-4-44−222222−2200000000000000−222222−22000000000000000000000000
χ574-4-44-200000022-222−22−222223−23−23230000006−6−66−222−2000000000000000000000000
χ584-4-44-200000022-222−22−2222−232323−23000000−666−6−222−2000000000000000000000000
χ594-4-44-200000022-2−222222−2223−23−2323000000−666−62−2−22000000000000000000000000
χ604-4-44-200000022-2−222222−22−232323−230000006−6−662−2−22000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.